Optimal length and signal amplification in weakly activated signal transduction cascades

Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals is obtained by choosing all the off rates equal and a universal finite optimal length.